CATSMLP: toward a robust and interpretable multilayer perceptron with sigmoid activation functions

Area of Science:

• Artificial Intelligence
• Machine Learning
• Fuzzy Logic

Background:

• Multilayer perceptrons (MLPs) with sigmoid activation present challenges in robustness and interpretability.
• Additive TS-type MLPs (ATSMLPs) offer interpretability via fuzzy IF-THEN rules but suffer from reduced robustness with increased layers.

Purpose of the Study:

• To introduce a novel MLP model, the cascaded ATSMLP (CATSMLP), designed to enhance robustness and interpretability.
• To theoretically establish CATSMLP as a universal approximator functionally equivalent to syllogistic fuzzy reasoning.

Main Methods:

• Organizing ATSMLPs in a cascaded structure to create the CATSMLP model.
• Proving the functional equivalence of CATSMLP to fuzzy inference systems based on syllogistic fuzzy reasoning.
• Demonstrating the enhanced robustness of CATSMLP compared to ATSMLP through theoretical analysis.

Main Results:

• The proposed CATSMLP model is a universal approximator.
• CATSMLP is theoretically equivalent to a fuzzy inference system using syllogistic fuzzy reasoning.
• Experimental results confirm that CATSMLP exhibits superior robustness over ATSMLP.

Conclusions:

• The CATSMLP model offers a more robust and interpretable alternative to traditional ATSMLPs.
• The cascaded architecture leverages syllogistic fuzzy reasoning for enhanced performance.
• This research contributes to advancing interpretable and robust deep learning models.